Mr. 0. Heaviside on the Extra Current. 137 



nA — vA— «%»? 



dQ r,- 1 - VtV cos mx -J-C * A62a 

 ^ = C — IT sin" • efc { 1+/V /I 



Wj 



| 2 (l-A),-g^'- tf -K 



/3 

 or 



dQ n -L _Vi7T cos tirx -— j3 

 ■dl =Qe * + ldsm—- e 2a -2*W- 



{(l-B'^4iV| -l)cos + (B'+ \/±iV? -A sin I 



where C is a constant current. Let the initial current be C, 

 then 



v 



r 2 | 



A= p . B' = 



therefore the expressions for the potential and current become 



11TX € 2a 



"=V"".^-|- r {(l+m)^-(l-.m) e --} ) . . (7) 



COS 



' I 2 



or 



sin iirx — -/ 1 . \tm' 



TT sm i9ra? - — / l . \tm' 



V=V „„—}—.€ 2a( COS H rSinlpr— , (8) 



cos / \ m' / 2a' y ' 



where 



and 



__£ 



c?Q ~ __' Viir cos iirx e ** , ** _^ N 

 or 



(9) 



dQ ~ _-_ Vwr cos ottce 2e 2a , £ m ' 



